Research Publications

Books

  1. Differential Geometry and Symmetric Spaces, 500 pp. Academic Press, New York, 1962. Russian translation, MIR, Moscow, 1964. Published by Amer. Math. Soc. in 2000. Review here. Readers' comments.
  2. Analysis on Lie Groups and Homogeneous Spaces, 70 p. Conference Board of Math. Science Lectures, Dartmouth 1971. Amer. Math. Soc. CBMS Monographs 1972. Second Edition 1977.
  3. Differential Geometry, Lie Groups and Symmetric Spaces, 656 pp. Academic Press, New York, 1978. Russian translation, Factorial Press, 2005. Published by Amer. Math. Soc. in 2001. Description at: AMS Bookstore Online.   Supplementary Note (Paper 98),   Expository Suggestions (Paper 99)
  4. The Radon Transform. Birkhäuser, Boston 1980, 202 pp. Russian translation, MIR, Moscow, 1983.
  5. Topics in Harmonic Analysis, 152 p. Birkhäuser, Boston, 1981.
  6. Groups and Geometric Analysis, 680 p. Academic Press, New York and Orlando, 1984. Russian translation, MIR, Moscow, 1987. Published by Amer. Math. Soc. in 2000. Description at: AMS Bookstore Online.   Supplementary Notes 1 (Paper No. 92),   Supplementary Notes 2 (Paper No. 93)
  7. Geometric Analysis on Symmetric Spaces, Mathematical Surveys and Monographs, Second Edition. Amer. Math. Soc. 2008, 637 pp.
    Here is a description at the Amazon Bookstore. Description of first edition can be found here. Errata
  8. (With Guðmundur Arnlaugsson) Stærðfræðingurinn Ólafur Daníelsson. Saga Brautryðjanda. Háskólaútgáfan, 1996.
  9. The Radon Transform, Second edition. Downloadable. Hardcover edition also available, published by Birkhauser Boston, 1999.
    Errata & Addenda Radon Transform. Description here. Review here.
  10. The Selected Works of Sigurdur Helgason, Description at: AMS Bookstore Online, Introduction and analytical comments. MAA Review.
  11. Integral Geometry and Radon Transforms, 301p, Springer, First Edition 2011. Reviews, Errata Front Cover Back Cover

Papers

  1. The derived algebra of a Banach algebra. Proc. Nat. Acad. Sci. USA 40 (l954), 994-995.
  2. Some problems in the theory of almost periodic functions, Math. Scand.3 (l955), 49-67.
  3. Multipliers of Banach algebras. Ann. of Math. 64 (l956), 240-254.
  4. 4. A characterization of the intersection of L1 spaces. Math. Scand. 4 (l956), 5-8.
  5. Topologies of group algebras and a theorem of Littlewood. Trans. Amer. Math. Soc. 86 (l957), 269-283.
  6. Partial differential equations on Lie groups. Thirteenth Scand. Math. Congr. Helsinki, l957, 110-115.
  7. Lacunary Fourier series on noncommutative groups. Proc. Amer. Math. Soc. 9 (l958), 782-790.
  8. On Riemannian curvature of homogeneous spaces. Proc. Amer. Math. Soc. 9 (l958), 831-838.
  9. Differential operators on homogeneous spaces. Acta Math. 102 (l959), 239-299.
  10. Some remarks on the exponential mapping of an affine connection. Math. Scand. 9 (l961), l29-l46.
  11. Some results on invariant theory. Bull. Amer. Math. Soc. 68 (l962), 367-371.
  12. Invariants and fundamental functions. Acta Math. 109 (l963), 241-258.
  13. Fundamental solutions of invariant differential operators on symmetric spaces. Bull. Amer. Math. Soc. 68 (l963), 778-781.
  14. Duality and Radon transform for symmetric spaces. Bull. Amer. Math. Soc. 69 (l963), 782-788.
  15. Duality and Radon transform for symmetric spaces. Amer. J. Math. 85 (l963), 667-692.
  16. Fundamental solutions of invariant differential operators on symmetric spaces. Amer. J. Math. 86 (l964), 565-601.
  17. A duality in integral geometry; some generalizations of the Radon transform. Bull. Amer. Math. Soc. 70 (l964), 435-446.
  18. The Radon transform on Euclidean spaces, compact two-point homogeneous spaces and Grassmann manifolds. Acta Math. 113 (l965), 153-180.
  19. Radon-Fourier transforms on symmetric spaces and related group representations. Bull. Amer. Math. Soc. 71 (l965), 757-763.
  20. A duality in integral geometry on symmetric spaces. Proc. U.S.- Japan Seminar in Differential Geometry, Kyoto, Japan, l965, 37-56. Nippon Hyronsha, Tokyo l966. In Book No. 10.
  21. Totally geodesic spheres in compact symmetric spaces. Math. Ann. 165 (l966), 309-317.
  22. An analog of the Paley-Wiener theorem for the Fourier transform on certain symmetric spaces. Math. Ann. 165 (1966), 297-308.
  23. (with A. Korányi) A Fatou-type theorem for harmonic functions on symmetric spaces. Bull. Amer. Math. Soc. 74 (l968), 258-263.
  24. Lie groups and symmetric spaces. Battelle Rencontres 1967, 1-71. W. A. Benjamin, Inc., New York l968.
  25. Some geometric properties of differential operators, Scientia Islandica, Anniversary Volume 1968, 41-43.
  26. (with K. Johnson) The bounded spherical functions on symmetric spaces. Advan. Math. 3 (l969), 586-593.
  27. Applications of the Radon transform to representations of semisimple Lie groups. Proc. Nat. Acad. Sci. USA 63 (1969), 643-647. In Book No. 10.
  28. A duality for symmetric spaces with applications to group representations. Advan. Math. 5 (l970), 1-154.
  29. Representations of semisimple Lie groups. CIME lectures, Montecatini 1970, Edition Cremonese, Rome, 1971. In Springer CIME Series, Vol. 82, 2011.
  30. Group representations and symmetric spaces. Proc. Internat. Congress Math. Nice 1970, Vol. 2. Gauthier-Villars, Paris 1971, 313-320. In Book No. 10.
  31. Conical distributions and group representations. Symmetric Spaces, Short courses presented at Washington Univerity, Marcel Dekker, Inc. New York, l972, 141-156.
  32. A formula for the radial part of the Laplace-Beltrami operator. J. Diff. Geometry 6 (l972), 411-419.
  33. Harmonic analysis in the non-Euclidean disk. Proc. Internat. Conf. on Harmonic Analysis, Univ. of Maryland 1971. Lecture Notes in Mathematics Vol. 266.
  34. Geometric reduction of differential operators. Symposia Mathematica 10 (1972), 107-115.
  35. Paley-Wiener theorems and surjectivity of invariant differential operators on symmetric spaces and Lie groups. Bull. Amer. Math. Soc. 79 (l973), 129-132.
  36. Functions on symmetric spaces. Proc. Sympos. Pure Math. Vol. 26, Amer. Math. Soc., Providence, R. I., 1973, 101-146.
  37. The surjectivity of invariant differential operators on symmetric spaces I. Ann. of Math. 98 (1973), 451-480.
  38. Spherical functions, spherical representations and correspondence theorems for the spherical Fourier transform, Colloque sur les fonctions sphériques et la théorie des groupes, Nancy, 5-9, 1971. Russian translation, Mathematika 17 (1973).
  39. Elie Cartan's Symmetriske Rum, Danish Math. Soc. Centennial Publication, 1973.
  40. Eigenspaces of the Laplacian; integral representations and irreducibility. J. Functional Anal. 17 (1974), 328-353.
  41. The eigenfunctions of the Laplacian on a two-point homogeneous space; integral representations and irreducibility. Proc. Sympos. Pure Math. Vol. 27. Amer. Math. Soc., Providence, R. I., 1975.
  42. Remarque sur R.G. McLenaghan: On the validity of Huygens principle for second order partial differential equations with four independent variables. I. Ann. Inst. Poincaré Sect. A 21 (1974),
  43. ibid. (1975.
  44. A duality for symmetric spaces with applications to group representations, II. Differential equations and eigenspace representations. Advances in Mathematics. 22 (1976), 187-219.
  45. Solvability of invariant differential operators on homogeneous manifolds. CIME seminar lecture Varenna 1975. Edizioni Cremonese. Roma, 1975. Also in Springer CIME Series Vol. 70, 2010.
  46. Solvability questions for invariant differential operators. Fifth International Colloquium on Group Theoretical Methods in Physics, Montreal, 1976. Academic Press 1977.
  47. Invariant differential equations on homogeneous manifolds. Bull. Amer. Math. Soc. 83 (1977), 751-774.
  48. Some results on eigenfunctions on symmetric spaces and eigenspace representations. Math. Scand. 41 (l977), 79-89.8
  49. A duality for symmetric spaces with applications to group representations. III. Tangent space analysis. Advan. Math. 36 (1980), 297-323.
  50. Invariant differential operators and eigenspace representations. In "Representations of Lie groups" by Atiyah et. al. London Mathematical Society, Lecture Note Series. 1979 236-286.
  51. Support of Radon transforms. Advan. Math. 38 (1980), 91-100.
  52. The X-ray transform on a symmetric space. Proc. Conf. Diff. Geometry and Global Analysis, Berlin 1979. Lecture Notes in Math. No.838 ,145-148, Springer Verlag, NewYork, 1981.
  53. Ranges of Radon Transforms. Proc. Symp. on Applied Math. Vol. 27, Amer. Math. Soc. 1982.
  54. The Range of the Radon Transform on Symmetric Spaces. Proc. Conference on "Representations of Reductive Lie Groups", Utah 1982, Birkhäuser, 1983.
  55. Topics in Geometric Fourier Analysis. In Proc. of Seminar on "Topics in Modern Harmonic Analyisis" Milano-Turin, 1982.
  56. Wave equations on homogeneous spaces. In Lie Group Representations III. Lecture Notes in Math. 1077, 254-287, Springer Verlag, New York, 1984.
  57. Operational properties of the Radon transform with applications. Proc. Conf. Differential Geometry and Applications, Nove Mesto Morave Czechoslovakia 1983. Publ. Univ. Karlova Praha, 1984.
  58. The Fourier transform on symmetric spaces. Asterisque 1985, 151-164.
  59. Some results on Radon transforms, Huygens Principle and X-ray transforms. Proc. AMS Conf. on Integral Geometry, Brunswick, 1984. Contemp. Math. No. 63 ,151-177 , Amer. Math. Soc. 1986.
  60. (with F. Gonzalez) Invariant differential operators on Grassmann manifolds. Advances in Math. 60 (1986), 81-91.
  61. Value-distribution theory for analytic almost periodic functions. The Harald Bohr Centenary. Proc. Symp. Copenhagen 1987, Munksgaard , Copenhagen 1989, 93-102. In Book No. 10.
  62. Response to Steele Prize Award. Notices Amer. Math. Soc. 35 (1988), 965-967.
  63. The totally geodesic Radon transform on constant curvature spaces. Arcata Conf. 1989 Contemp. Math. 113 (1990) 141-149.
  64. Some results on invariant differential operators on symmetric spaces. Amer. J. Math. 114 (1992), 789-811.
  65. Invariant differential operators and Weyl group invariants p.193-200 in "Harmonic Analysis on Reductive Groups" Ed. by W. Barker and P. Sally. Birkhäuser, Boston 1991.
  66. A Centennial: Wilhelm Killing and the exceptional groups. Math. Intelligencer, 12 (1990) 54-57.
  67. Geometric and Analytic Features of the Radon Transform. Mitteilungen der Math. Gesellschaft, Hamburg, 12 (1991) 977-988 (1992) .
  68. Support Theorems in Integral Geometry and their Applications . Proc. 1990 AMS Summer Inst. on Differential Geometry, Vol. 54 (1993).
  69. Tveir Töframenn Rúmfræðinnar, Poncelet og Jacobi. Icelandic Math. Soc. Bulletin 1991, 6-17.
  70. The Flat Horocycle Transform for a Symmetric Space. Advan. Math. 91 (1992), 232-251.
  71. Radon Vörpunin, Afbrigði og Notkun, Leifur Asgeirsson Memorial Volume. Háskólaútgáfan, Reykjavik 1998.
  72. Huygens' Principle for Wave Equations on Symmetric Spaces. J. Funct. Anal. 107 (1992) 279-288.
  73. The Wave Equation on Symmetric Spaces. Proc. Wigner Symposium, Goslar 1991. In "Classical and Quantum Suystems" Internat. Wigner Symp. Goslar 1991. World Scientific. Singapore 1993.
  74. Sophus Lie and the role of Lie groups in mathematics. Report of the 14. Nordic LMFK-congress Reykjavík , 1990.
  75. The Radon transform for double fibrations; examples and viewpoints. Proc. of Symposium "75 years of Radon Transform" Vienna, Sept. 1992 . International Press, Inc. Boston, 1994.
  76. The Fourier Transform on Symmetric Spaces and Applications. Proc. Conf. Differential Geometry and Applications, Opava, Czechoslovakia, August , 1992, 23-28.
  77. Sophus Lie, the Mathematician, Proc. of Sophus Lie Memorial Conference, Oslo, August, 1992, Scandinavian University Press, Oslo, Norway, 1994, 3-21.
  78. Harish-Chandra's c-function; a mathematical jewel. In "Noncompact Lie Groups and Some of Their Applications". Proc. Nato Conference San Antonio, Jan. 1993. Kluver Acad. Publishers 1994, 55-67. Also in No. 83.
  79. Radon Transforms and Wave Equations. C.I.M.E. 1996. Springer Lecture Notes No. 1684, (1998) pp. 99-121
  80. Orbital Integrals, Symmetric Fourier Analysis and Eigenspace Representations. Proc. Symp. Pure Math. Amer. Math. Soc. Vol. 61 (1997) pp.167-189.
  81. P. Günther’s work on Hadamard’s conjecture. Zeitschr. Anal. Anw. 16 (1997),5-6.
  82. Integral Geometry and Multitemporal Wave Equations. Comm. Pure and Appl. Math. 51 (1998) 1035-1071.
  83. (With H. Schlichtkrull) The Paley-Wiener Space for the Multitemporal Wave Equation. Comm. Pure and Appl. Math. 52 (1999) 49-52.
  84. Harish-Chandra and his Mathematical Legacy. Some Personal Recollections. Current Science Indian Academy of Sciences. 1998.
  85. Reprint of No. 76. Amer. Math. Soc. Proc. Symp. Pure Math. No. 68. (2000) , 273-283.
  86. Harish-Chandra Memorial Talk, ibid. 43-45.
  87. The Non-Euclidean World. History, Geometry and Analysis. (In Icelandic). See also Publiction 88.
  88. The Fourier Transform on Symmetric Spaces. Applications to Classical and Multitemporal Wave Equations. Amer. Math. Soc. Proc. Symp.Pure Math. (to appear).
  89. Rúmfræði og Raunveruleikinn. Icelandic Math Society Bulletin, 2000. pp. 1-12.
  90. Non-Euclidean Analysis, in “Non-Euclidean Geometries”. Proceedings of the Janos Bolyai Mem. Conf., Budapest, July, 2002. Prékopa and Molnár Eds. Springer, 2006. p.367-384.
  91. Remarks on B. Rubin, Radon, Cosine and Sine Transforms on Real Hyperbolic Space. Advan. Math. (192 (2005) page 225).
  92. The Abel, Fourier and Radon Transforms on Symmetric Spaces. Indagationes Mathematicae. 16 (2005) 531-551.
  93. Hörmander's Topological Paley-Wiener Theorem. Included in Chapter VII of Book 11.
  94. Supplementary Note 1 to Book 6: “Groups and Geometric Analysis” (antipodal Radon transform and Schwartz space theorem)
  95. Supplementary Note 2 to Book 6: "Groups and Geometric Analysis" (weight theory and a short proof of the Borel-Weil theorem)
  96. The Inversion of the X-ray Transform on a Compact Symmetric Space. Journal of Lie Theory. 17 (2007) 307-315.
  97. Notes on Complex Analysis. In MIT Open Course Ware, Course 18.112: Complex Analysis. Supplements to Ahlfors' text.
  98. Support Theorems for Horocycles on Hyperbolic Spaces. Pure Appl. Math Q. 8(2012) 4 (921-927)
  99. Some Personal Remarks on the Radon Transform. In "Contemporary Mathematics," No. 598, 3-19, Amer. Math. Soc. 2013.
  100. Supplementary Note to Book 3 Coverings etc.
  101. Expository Suggestions to Book 3
  102. The Bounded Spherical Functions on the Cartan Motion Group. arXiv: 1503.07598v1, March 2015
  103. Spherical Functions on Riemannian Symmetric Spaces, arXiv: 1707.06124v3, 11. Sept. 2017